Properties

Label 8035.2.a.b.1.19
Level $8035$
Weight $2$
Character 8035.1
Self dual yes
Analytic conductor $64.160$
Analytic rank $1$
Dimension $114$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8035,2,Mod(1,8035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8035, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8035.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8035.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(1\)
Dimension: \(114\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 8035.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.12278 q^{2} -3.22748 q^{3} +2.50621 q^{4} +1.00000 q^{5} +6.85125 q^{6} +1.25827 q^{7} -1.07458 q^{8} +7.41664 q^{9} +O(q^{10})\) \(q-2.12278 q^{2} -3.22748 q^{3} +2.50621 q^{4} +1.00000 q^{5} +6.85125 q^{6} +1.25827 q^{7} -1.07458 q^{8} +7.41664 q^{9} -2.12278 q^{10} -5.28754 q^{11} -8.08875 q^{12} -5.41589 q^{13} -2.67103 q^{14} -3.22748 q^{15} -2.73133 q^{16} +0.0963515 q^{17} -15.7439 q^{18} +1.09592 q^{19} +2.50621 q^{20} -4.06103 q^{21} +11.2243 q^{22} +2.58108 q^{23} +3.46818 q^{24} +1.00000 q^{25} +11.4968 q^{26} -14.2546 q^{27} +3.15348 q^{28} -9.69197 q^{29} +6.85125 q^{30} -5.73717 q^{31} +7.94717 q^{32} +17.0654 q^{33} -0.204533 q^{34} +1.25827 q^{35} +18.5877 q^{36} +7.95947 q^{37} -2.32640 q^{38} +17.4797 q^{39} -1.07458 q^{40} +0.183699 q^{41} +8.62069 q^{42} +8.82458 q^{43} -13.2517 q^{44} +7.41664 q^{45} -5.47907 q^{46} +11.1082 q^{47} +8.81532 q^{48} -5.41677 q^{49} -2.12278 q^{50} -0.310973 q^{51} -13.5734 q^{52} +4.26606 q^{53} +30.2595 q^{54} -5.28754 q^{55} -1.35210 q^{56} -3.53706 q^{57} +20.5740 q^{58} -0.728348 q^{59} -8.08875 q^{60} +0.00924476 q^{61} +12.1788 q^{62} +9.33211 q^{63} -11.4075 q^{64} -5.41589 q^{65} -36.2262 q^{66} -3.46467 q^{67} +0.241477 q^{68} -8.33039 q^{69} -2.67103 q^{70} -7.12503 q^{71} -7.96975 q^{72} -7.57368 q^{73} -16.8962 q^{74} -3.22748 q^{75} +2.74660 q^{76} -6.65313 q^{77} -37.1056 q^{78} +15.5923 q^{79} -2.73133 q^{80} +23.7567 q^{81} -0.389952 q^{82} +10.1024 q^{83} -10.1778 q^{84} +0.0963515 q^{85} -18.7327 q^{86} +31.2807 q^{87} +5.68186 q^{88} +6.85878 q^{89} -15.7439 q^{90} -6.81462 q^{91} +6.46873 q^{92} +18.5166 q^{93} -23.5803 q^{94} +1.09592 q^{95} -25.6494 q^{96} +2.35225 q^{97} +11.4986 q^{98} -39.2158 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.12278 −1.50103 −0.750517 0.660851i \(-0.770196\pi\)
−0.750517 + 0.660851i \(0.770196\pi\)
\(3\) −3.22748 −1.86339 −0.931694 0.363244i \(-0.881669\pi\)
−0.931694 + 0.363244i \(0.881669\pi\)
\(4\) 2.50621 1.25311
\(5\) 1.00000 0.447214
\(6\) 6.85125 2.79701
\(7\) 1.25827 0.475580 0.237790 0.971317i \(-0.423577\pi\)
0.237790 + 0.971317i \(0.423577\pi\)
\(8\) −1.07458 −0.379920
\(9\) 7.41664 2.47221
\(10\) −2.12278 −0.671283
\(11\) −5.28754 −1.59425 −0.797126 0.603813i \(-0.793648\pi\)
−0.797126 + 0.603813i \(0.793648\pi\)
\(12\) −8.08875 −2.33502
\(13\) −5.41589 −1.50210 −0.751048 0.660247i \(-0.770451\pi\)
−0.751048 + 0.660247i \(0.770451\pi\)
\(14\) −2.67103 −0.713862
\(15\) −3.22748 −0.833332
\(16\) −2.73133 −0.682832
\(17\) 0.0963515 0.0233687 0.0116843 0.999932i \(-0.496281\pi\)
0.0116843 + 0.999932i \(0.496281\pi\)
\(18\) −15.7439 −3.71088
\(19\) 1.09592 0.251421 0.125710 0.992067i \(-0.459879\pi\)
0.125710 + 0.992067i \(0.459879\pi\)
\(20\) 2.50621 0.560406
\(21\) −4.06103 −0.886189
\(22\) 11.2243 2.39303
\(23\) 2.58108 0.538192 0.269096 0.963113i \(-0.413275\pi\)
0.269096 + 0.963113i \(0.413275\pi\)
\(24\) 3.46818 0.707938
\(25\) 1.00000 0.200000
\(26\) 11.4968 2.25470
\(27\) −14.2546 −2.74331
\(28\) 3.15348 0.595951
\(29\) −9.69197 −1.79975 −0.899877 0.436143i \(-0.856344\pi\)
−0.899877 + 0.436143i \(0.856344\pi\)
\(30\) 6.85125 1.25086
\(31\) −5.73717 −1.03043 −0.515213 0.857062i \(-0.672287\pi\)
−0.515213 + 0.857062i \(0.672287\pi\)
\(32\) 7.94717 1.40487
\(33\) 17.0654 2.97071
\(34\) −0.204533 −0.0350772
\(35\) 1.25827 0.212686
\(36\) 18.5877 3.09795
\(37\) 7.95947 1.30853 0.654264 0.756266i \(-0.272978\pi\)
0.654264 + 0.756266i \(0.272978\pi\)
\(38\) −2.32640 −0.377391
\(39\) 17.4797 2.79899
\(40\) −1.07458 −0.169905
\(41\) 0.183699 0.0286889 0.0143444 0.999897i \(-0.495434\pi\)
0.0143444 + 0.999897i \(0.495434\pi\)
\(42\) 8.62069 1.33020
\(43\) 8.82458 1.34574 0.672868 0.739762i \(-0.265062\pi\)
0.672868 + 0.739762i \(0.265062\pi\)
\(44\) −13.2517 −1.99777
\(45\) 7.41664 1.10561
\(46\) −5.47907 −0.807845
\(47\) 11.1082 1.62030 0.810150 0.586223i \(-0.199386\pi\)
0.810150 + 0.586223i \(0.199386\pi\)
\(48\) 8.81532 1.27238
\(49\) −5.41677 −0.773824
\(50\) −2.12278 −0.300207
\(51\) −0.310973 −0.0435449
\(52\) −13.5734 −1.88229
\(53\) 4.26606 0.585989 0.292994 0.956114i \(-0.405348\pi\)
0.292994 + 0.956114i \(0.405348\pi\)
\(54\) 30.2595 4.11780
\(55\) −5.28754 −0.712972
\(56\) −1.35210 −0.180682
\(57\) −3.53706 −0.468495
\(58\) 20.5740 2.70149
\(59\) −0.728348 −0.0948228 −0.0474114 0.998875i \(-0.515097\pi\)
−0.0474114 + 0.998875i \(0.515097\pi\)
\(60\) −8.08875 −1.04425
\(61\) 0.00924476 0.00118367 0.000591835 1.00000i \(-0.499812\pi\)
0.000591835 1.00000i \(0.499812\pi\)
\(62\) 12.1788 1.54671
\(63\) 9.33211 1.17573
\(64\) −11.4075 −1.42593
\(65\) −5.41589 −0.671758
\(66\) −36.2262 −4.45914
\(67\) −3.46467 −0.423277 −0.211639 0.977348i \(-0.567880\pi\)
−0.211639 + 0.977348i \(0.567880\pi\)
\(68\) 0.241477 0.0292834
\(69\) −8.33039 −1.00286
\(70\) −2.67103 −0.319249
\(71\) −7.12503 −0.845586 −0.422793 0.906226i \(-0.638950\pi\)
−0.422793 + 0.906226i \(0.638950\pi\)
\(72\) −7.96975 −0.939244
\(73\) −7.57368 −0.886432 −0.443216 0.896415i \(-0.646163\pi\)
−0.443216 + 0.896415i \(0.646163\pi\)
\(74\) −16.8962 −1.96415
\(75\) −3.22748 −0.372678
\(76\) 2.74660 0.315057
\(77\) −6.65313 −0.758194
\(78\) −37.1056 −4.20138
\(79\) 15.5923 1.75427 0.877136 0.480241i \(-0.159451\pi\)
0.877136 + 0.480241i \(0.159451\pi\)
\(80\) −2.73133 −0.305372
\(81\) 23.7567 2.63963
\(82\) −0.389952 −0.0430630
\(83\) 10.1024 1.10889 0.554444 0.832221i \(-0.312931\pi\)
0.554444 + 0.832221i \(0.312931\pi\)
\(84\) −10.1778 −1.11049
\(85\) 0.0963515 0.0104508
\(86\) −18.7327 −2.02000
\(87\) 31.2807 3.35364
\(88\) 5.68186 0.605688
\(89\) 6.85878 0.727030 0.363515 0.931588i \(-0.381577\pi\)
0.363515 + 0.931588i \(0.381577\pi\)
\(90\) −15.7439 −1.65956
\(91\) −6.81462 −0.714366
\(92\) 6.46873 0.674412
\(93\) 18.5166 1.92008
\(94\) −23.5803 −2.43213
\(95\) 1.09592 0.112439
\(96\) −25.6494 −2.61783
\(97\) 2.35225 0.238835 0.119418 0.992844i \(-0.461897\pi\)
0.119418 + 0.992844i \(0.461897\pi\)
\(98\) 11.4986 1.16154
\(99\) −39.2158 −3.94133
\(100\) 2.50621 0.250621
\(101\) −2.37026 −0.235850 −0.117925 0.993023i \(-0.537624\pi\)
−0.117925 + 0.993023i \(0.537624\pi\)
\(102\) 0.660128 0.0653624
\(103\) 16.8025 1.65560 0.827800 0.561024i \(-0.189592\pi\)
0.827800 + 0.561024i \(0.189592\pi\)
\(104\) 5.81978 0.570677
\(105\) −4.06103 −0.396316
\(106\) −9.05593 −0.879590
\(107\) −16.2024 −1.56635 −0.783173 0.621804i \(-0.786400\pi\)
−0.783173 + 0.621804i \(0.786400\pi\)
\(108\) −35.7251 −3.43765
\(109\) −14.4627 −1.38528 −0.692638 0.721286i \(-0.743552\pi\)
−0.692638 + 0.721286i \(0.743552\pi\)
\(110\) 11.2243 1.07020
\(111\) −25.6890 −2.43830
\(112\) −3.43674 −0.324741
\(113\) −5.31068 −0.499586 −0.249793 0.968299i \(-0.580363\pi\)
−0.249793 + 0.968299i \(0.580363\pi\)
\(114\) 7.50841 0.703227
\(115\) 2.58108 0.240687
\(116\) −24.2901 −2.25528
\(117\) −40.1677 −3.71351
\(118\) 1.54612 0.142332
\(119\) 0.121236 0.0111137
\(120\) 3.46818 0.316600
\(121\) 16.9581 1.54164
\(122\) −0.0196246 −0.00177673
\(123\) −0.592884 −0.0534585
\(124\) −14.3786 −1.29123
\(125\) 1.00000 0.0894427
\(126\) −19.8100 −1.76482
\(127\) −1.86927 −0.165871 −0.0829353 0.996555i \(-0.526429\pi\)
−0.0829353 + 0.996555i \(0.526429\pi\)
\(128\) 8.32125 0.735501
\(129\) −28.4812 −2.50763
\(130\) 11.4968 1.00833
\(131\) −11.5178 −1.00631 −0.503156 0.864196i \(-0.667828\pi\)
−0.503156 + 0.864196i \(0.667828\pi\)
\(132\) 42.7696 3.72261
\(133\) 1.37896 0.119571
\(134\) 7.35475 0.635353
\(135\) −14.2546 −1.22684
\(136\) −0.103537 −0.00887823
\(137\) −0.667543 −0.0570320 −0.0285160 0.999593i \(-0.509078\pi\)
−0.0285160 + 0.999593i \(0.509078\pi\)
\(138\) 17.6836 1.50533
\(139\) 8.98399 0.762012 0.381006 0.924573i \(-0.375578\pi\)
0.381006 + 0.924573i \(0.375578\pi\)
\(140\) 3.15348 0.266518
\(141\) −35.8516 −3.01925
\(142\) 15.1249 1.26925
\(143\) 28.6367 2.39472
\(144\) −20.2573 −1.68811
\(145\) −9.69197 −0.804875
\(146\) 16.0773 1.33057
\(147\) 17.4825 1.44193
\(148\) 19.9481 1.63972
\(149\) 21.2490 1.74078 0.870392 0.492359i \(-0.163865\pi\)
0.870392 + 0.492359i \(0.163865\pi\)
\(150\) 6.85125 0.559402
\(151\) −2.90523 −0.236425 −0.118212 0.992988i \(-0.537716\pi\)
−0.118212 + 0.992988i \(0.537716\pi\)
\(152\) −1.17765 −0.0955198
\(153\) 0.714605 0.0577724
\(154\) 14.1231 1.13808
\(155\) −5.73717 −0.460821
\(156\) 43.8078 3.50743
\(157\) −10.6639 −0.851071 −0.425535 0.904942i \(-0.639914\pi\)
−0.425535 + 0.904942i \(0.639914\pi\)
\(158\) −33.0991 −2.63322
\(159\) −13.7686 −1.09192
\(160\) 7.94717 0.628279
\(161\) 3.24768 0.255953
\(162\) −50.4303 −3.96218
\(163\) 12.3766 0.969407 0.484703 0.874679i \(-0.338928\pi\)
0.484703 + 0.874679i \(0.338928\pi\)
\(164\) 0.460387 0.0359502
\(165\) 17.0654 1.32854
\(166\) −21.4453 −1.66448
\(167\) −15.6367 −1.21001 −0.605004 0.796223i \(-0.706828\pi\)
−0.605004 + 0.796223i \(0.706828\pi\)
\(168\) 4.36388 0.336681
\(169\) 16.3318 1.25629
\(170\) −0.204533 −0.0156870
\(171\) 8.12803 0.621566
\(172\) 22.1163 1.68635
\(173\) −11.0772 −0.842187 −0.421093 0.907017i \(-0.638354\pi\)
−0.421093 + 0.907017i \(0.638354\pi\)
\(174\) −66.4021 −5.03393
\(175\) 1.25827 0.0951159
\(176\) 14.4420 1.08861
\(177\) 2.35073 0.176692
\(178\) −14.5597 −1.09130
\(179\) 11.3970 0.851851 0.425925 0.904758i \(-0.359949\pi\)
0.425925 + 0.904758i \(0.359949\pi\)
\(180\) 18.5877 1.38544
\(181\) 6.95468 0.516938 0.258469 0.966020i \(-0.416782\pi\)
0.258469 + 0.966020i \(0.416782\pi\)
\(182\) 14.4660 1.07229
\(183\) −0.0298373 −0.00220564
\(184\) −2.77357 −0.204470
\(185\) 7.95947 0.585192
\(186\) −39.3068 −2.88211
\(187\) −0.509462 −0.0372556
\(188\) 27.8395 2.03041
\(189\) −17.9361 −1.30466
\(190\) −2.32640 −0.168775
\(191\) 4.90468 0.354890 0.177445 0.984131i \(-0.443217\pi\)
0.177445 + 0.984131i \(0.443217\pi\)
\(192\) 36.8174 2.65707
\(193\) 3.12752 0.225124 0.112562 0.993645i \(-0.464094\pi\)
0.112562 + 0.993645i \(0.464094\pi\)
\(194\) −4.99332 −0.358500
\(195\) 17.4797 1.25175
\(196\) −13.5756 −0.969683
\(197\) −15.1557 −1.07980 −0.539899 0.841730i \(-0.681537\pi\)
−0.539899 + 0.841730i \(0.681537\pi\)
\(198\) 83.2466 5.91608
\(199\) 22.9484 1.62677 0.813385 0.581725i \(-0.197622\pi\)
0.813385 + 0.581725i \(0.197622\pi\)
\(200\) −1.07458 −0.0759840
\(201\) 11.1822 0.788729
\(202\) 5.03156 0.354019
\(203\) −12.1951 −0.855926
\(204\) −0.779364 −0.0545664
\(205\) 0.183699 0.0128301
\(206\) −35.6681 −2.48511
\(207\) 19.1429 1.33053
\(208\) 14.7926 1.02568
\(209\) −5.79471 −0.400828
\(210\) 8.62069 0.594884
\(211\) 2.35450 0.162091 0.0810453 0.996710i \(-0.474174\pi\)
0.0810453 + 0.996710i \(0.474174\pi\)
\(212\) 10.6917 0.734306
\(213\) 22.9959 1.57565
\(214\) 34.3942 2.35114
\(215\) 8.82458 0.601832
\(216\) 15.3177 1.04224
\(217\) −7.21888 −0.490050
\(218\) 30.7012 2.07935
\(219\) 24.4439 1.65177
\(220\) −13.2517 −0.893428
\(221\) −0.521829 −0.0351020
\(222\) 54.5323 3.65997
\(223\) 11.5823 0.775607 0.387803 0.921742i \(-0.373234\pi\)
0.387803 + 0.921742i \(0.373234\pi\)
\(224\) 9.99965 0.668130
\(225\) 7.41664 0.494443
\(226\) 11.2734 0.749896
\(227\) −9.71403 −0.644743 −0.322371 0.946613i \(-0.604480\pi\)
−0.322371 + 0.946613i \(0.604480\pi\)
\(228\) −8.86461 −0.587073
\(229\) 2.57391 0.170089 0.0850444 0.996377i \(-0.472897\pi\)
0.0850444 + 0.996377i \(0.472897\pi\)
\(230\) −5.47907 −0.361279
\(231\) 21.4728 1.41281
\(232\) 10.4148 0.683763
\(233\) −12.3695 −0.810354 −0.405177 0.914238i \(-0.632790\pi\)
−0.405177 + 0.914238i \(0.632790\pi\)
\(234\) 85.2673 5.57410
\(235\) 11.1082 0.724620
\(236\) −1.82539 −0.118823
\(237\) −50.3239 −3.26889
\(238\) −0.257357 −0.0166820
\(239\) 22.7696 1.47284 0.736420 0.676524i \(-0.236515\pi\)
0.736420 + 0.676524i \(0.236515\pi\)
\(240\) 8.81532 0.569026
\(241\) −2.16627 −0.139542 −0.0697709 0.997563i \(-0.522227\pi\)
−0.0697709 + 0.997563i \(0.522227\pi\)
\(242\) −35.9983 −2.31406
\(243\) −33.9103 −2.17535
\(244\) 0.0231693 0.00148326
\(245\) −5.41677 −0.346065
\(246\) 1.25856 0.0802431
\(247\) −5.93537 −0.377658
\(248\) 6.16503 0.391480
\(249\) −32.6055 −2.06629
\(250\) −2.12278 −0.134257
\(251\) −12.4537 −0.786069 −0.393035 0.919524i \(-0.628575\pi\)
−0.393035 + 0.919524i \(0.628575\pi\)
\(252\) 23.3882 1.47332
\(253\) −13.6476 −0.858015
\(254\) 3.96805 0.248978
\(255\) −0.310973 −0.0194739
\(256\) 5.15073 0.321921
\(257\) 28.4790 1.77647 0.888236 0.459388i \(-0.151931\pi\)
0.888236 + 0.459388i \(0.151931\pi\)
\(258\) 60.4594 3.76404
\(259\) 10.0151 0.622310
\(260\) −13.5734 −0.841784
\(261\) −71.8819 −4.44938
\(262\) 24.4497 1.51051
\(263\) −18.2807 −1.12724 −0.563618 0.826035i \(-0.690591\pi\)
−0.563618 + 0.826035i \(0.690591\pi\)
\(264\) −18.3381 −1.12863
\(265\) 4.26606 0.262062
\(266\) −2.92722 −0.179480
\(267\) −22.1366 −1.35474
\(268\) −8.68320 −0.530411
\(269\) 7.29726 0.444922 0.222461 0.974942i \(-0.428591\pi\)
0.222461 + 0.974942i \(0.428591\pi\)
\(270\) 30.2595 1.84154
\(271\) 13.1334 0.797795 0.398897 0.916996i \(-0.369393\pi\)
0.398897 + 0.916996i \(0.369393\pi\)
\(272\) −0.263168 −0.0159569
\(273\) 21.9941 1.33114
\(274\) 1.41705 0.0856070
\(275\) −5.28754 −0.318851
\(276\) −20.8777 −1.25669
\(277\) 12.6410 0.759526 0.379763 0.925084i \(-0.376005\pi\)
0.379763 + 0.925084i \(0.376005\pi\)
\(278\) −19.0711 −1.14381
\(279\) −42.5506 −2.54744
\(280\) −1.35210 −0.0808035
\(281\) −7.16052 −0.427161 −0.213580 0.976925i \(-0.568513\pi\)
−0.213580 + 0.976925i \(0.568513\pi\)
\(282\) 76.1051 4.53199
\(283\) 3.22701 0.191826 0.0959130 0.995390i \(-0.469423\pi\)
0.0959130 + 0.995390i \(0.469423\pi\)
\(284\) −17.8568 −1.05961
\(285\) −3.53706 −0.209517
\(286\) −60.7895 −3.59456
\(287\) 0.231142 0.0136439
\(288\) 58.9414 3.47315
\(289\) −16.9907 −0.999454
\(290\) 20.5740 1.20814
\(291\) −7.59186 −0.445042
\(292\) −18.9812 −1.11079
\(293\) 4.23600 0.247470 0.123735 0.992315i \(-0.460513\pi\)
0.123735 + 0.992315i \(0.460513\pi\)
\(294\) −37.1116 −2.16439
\(295\) −0.728348 −0.0424060
\(296\) −8.55305 −0.497136
\(297\) 75.3720 4.37352
\(298\) −45.1070 −2.61298
\(299\) −13.9788 −0.808417
\(300\) −8.08875 −0.467004
\(301\) 11.1037 0.640005
\(302\) 6.16718 0.354882
\(303\) 7.64998 0.439480
\(304\) −2.99331 −0.171678
\(305\) 0.00924476 0.000529354 0
\(306\) −1.51695 −0.0867184
\(307\) 2.50213 0.142804 0.0714019 0.997448i \(-0.477253\pi\)
0.0714019 + 0.997448i \(0.477253\pi\)
\(308\) −16.6741 −0.950097
\(309\) −54.2298 −3.08502
\(310\) 12.1788 0.691708
\(311\) 7.13749 0.404730 0.202365 0.979310i \(-0.435137\pi\)
0.202365 + 0.979310i \(0.435137\pi\)
\(312\) −18.7832 −1.06339
\(313\) 16.0884 0.909370 0.454685 0.890652i \(-0.349752\pi\)
0.454685 + 0.890652i \(0.349752\pi\)
\(314\) 22.6371 1.27749
\(315\) 9.33211 0.525805
\(316\) 39.0776 2.19829
\(317\) 21.5958 1.21294 0.606472 0.795105i \(-0.292584\pi\)
0.606472 + 0.795105i \(0.292584\pi\)
\(318\) 29.2279 1.63902
\(319\) 51.2467 2.86926
\(320\) −11.4075 −0.637697
\(321\) 52.2930 2.91871
\(322\) −6.89413 −0.384195
\(323\) 0.105593 0.00587537
\(324\) 59.5392 3.30774
\(325\) −5.41589 −0.300419
\(326\) −26.2728 −1.45511
\(327\) 46.6781 2.58131
\(328\) −0.197398 −0.0108995
\(329\) 13.9771 0.770581
\(330\) −36.2262 −1.99419
\(331\) 15.5622 0.855378 0.427689 0.903926i \(-0.359328\pi\)
0.427689 + 0.903926i \(0.359328\pi\)
\(332\) 25.3189 1.38955
\(333\) 59.0325 3.23496
\(334\) 33.1934 1.81626
\(335\) −3.46467 −0.189295
\(336\) 11.0920 0.605119
\(337\) −24.6361 −1.34201 −0.671007 0.741451i \(-0.734138\pi\)
−0.671007 + 0.741451i \(0.734138\pi\)
\(338\) −34.6689 −1.88574
\(339\) 17.1401 0.930923
\(340\) 0.241477 0.0130959
\(341\) 30.3355 1.64276
\(342\) −17.2541 −0.932993
\(343\) −15.6236 −0.843595
\(344\) −9.48268 −0.511272
\(345\) −8.33039 −0.448493
\(346\) 23.5146 1.26415
\(347\) 6.32537 0.339564 0.169782 0.985482i \(-0.445694\pi\)
0.169782 + 0.985482i \(0.445694\pi\)
\(348\) 78.3960 4.20247
\(349\) −12.8451 −0.687581 −0.343790 0.939046i \(-0.611711\pi\)
−0.343790 + 0.939046i \(0.611711\pi\)
\(350\) −2.67103 −0.142772
\(351\) 77.2015 4.12071
\(352\) −42.0210 −2.23973
\(353\) 4.23655 0.225489 0.112744 0.993624i \(-0.464036\pi\)
0.112744 + 0.993624i \(0.464036\pi\)
\(354\) −4.99009 −0.265220
\(355\) −7.12503 −0.378157
\(356\) 17.1896 0.911045
\(357\) −0.391286 −0.0207091
\(358\) −24.1933 −1.27866
\(359\) 24.9326 1.31589 0.657945 0.753066i \(-0.271426\pi\)
0.657945 + 0.753066i \(0.271426\pi\)
\(360\) −7.96975 −0.420043
\(361\) −17.7990 −0.936788
\(362\) −14.7633 −0.775941
\(363\) −54.7318 −2.87268
\(364\) −17.0789 −0.895176
\(365\) −7.57368 −0.396425
\(366\) 0.0633382 0.00331074
\(367\) 5.07470 0.264897 0.132448 0.991190i \(-0.457716\pi\)
0.132448 + 0.991190i \(0.457716\pi\)
\(368\) −7.04978 −0.367495
\(369\) 1.36243 0.0709251
\(370\) −16.8962 −0.878393
\(371\) 5.36784 0.278684
\(372\) 46.4066 2.40607
\(373\) 12.1357 0.628364 0.314182 0.949363i \(-0.398270\pi\)
0.314182 + 0.949363i \(0.398270\pi\)
\(374\) 1.08148 0.0559219
\(375\) −3.22748 −0.166666
\(376\) −11.9366 −0.615584
\(377\) 52.4906 2.70340
\(378\) 38.0745 1.95834
\(379\) −33.1978 −1.70525 −0.852627 0.522519i \(-0.824992\pi\)
−0.852627 + 0.522519i \(0.824992\pi\)
\(380\) 2.74660 0.140898
\(381\) 6.03303 0.309081
\(382\) −10.4116 −0.532702
\(383\) 13.5513 0.692437 0.346219 0.938154i \(-0.387466\pi\)
0.346219 + 0.938154i \(0.387466\pi\)
\(384\) −26.8567 −1.37052
\(385\) −6.65313 −0.339075
\(386\) −6.63904 −0.337918
\(387\) 65.4488 3.32695
\(388\) 5.89524 0.299286
\(389\) −29.1973 −1.48036 −0.740181 0.672407i \(-0.765260\pi\)
−0.740181 + 0.672407i \(0.765260\pi\)
\(390\) −37.1056 −1.87891
\(391\) 0.248691 0.0125768
\(392\) 5.82073 0.293991
\(393\) 37.1734 1.87515
\(394\) 32.1722 1.62081
\(395\) 15.5923 0.784535
\(396\) −98.2830 −4.93891
\(397\) 3.26900 0.164066 0.0820332 0.996630i \(-0.473859\pi\)
0.0820332 + 0.996630i \(0.473859\pi\)
\(398\) −48.7146 −2.44184
\(399\) −4.45056 −0.222806
\(400\) −2.73133 −0.136566
\(401\) −26.8559 −1.34112 −0.670559 0.741857i \(-0.733946\pi\)
−0.670559 + 0.741857i \(0.733946\pi\)
\(402\) −23.7373 −1.18391
\(403\) 31.0719 1.54780
\(404\) −5.94038 −0.295545
\(405\) 23.7567 1.18048
\(406\) 25.8875 1.28478
\(407\) −42.0860 −2.08613
\(408\) 0.334164 0.0165436
\(409\) −35.7439 −1.76742 −0.883711 0.468033i \(-0.844963\pi\)
−0.883711 + 0.468033i \(0.844963\pi\)
\(410\) −0.389952 −0.0192584
\(411\) 2.15448 0.106273
\(412\) 42.1106 2.07464
\(413\) −0.916454 −0.0450958
\(414\) −40.6363 −1.99717
\(415\) 10.1024 0.495909
\(416\) −43.0410 −2.11026
\(417\) −28.9957 −1.41992
\(418\) 12.3009 0.601657
\(419\) −12.9463 −0.632470 −0.316235 0.948681i \(-0.602419\pi\)
−0.316235 + 0.948681i \(0.602419\pi\)
\(420\) −10.1778 −0.496626
\(421\) 23.5042 1.14552 0.572762 0.819721i \(-0.305872\pi\)
0.572762 + 0.819721i \(0.305872\pi\)
\(422\) −4.99810 −0.243304
\(423\) 82.3857 4.00573
\(424\) −4.58421 −0.222629
\(425\) 0.0963515 0.00467374
\(426\) −48.8154 −2.36511
\(427\) 0.0116324 0.000562930 0
\(428\) −40.6066 −1.96280
\(429\) −92.4245 −4.46230
\(430\) −18.7327 −0.903370
\(431\) −3.56689 −0.171811 −0.0859056 0.996303i \(-0.527378\pi\)
−0.0859056 + 0.996303i \(0.527378\pi\)
\(432\) 38.9341 1.87322
\(433\) −3.60278 −0.173139 −0.0865693 0.996246i \(-0.527590\pi\)
−0.0865693 + 0.996246i \(0.527590\pi\)
\(434\) 15.3241 0.735582
\(435\) 31.2807 1.49979
\(436\) −36.2466 −1.73590
\(437\) 2.82865 0.135313
\(438\) −51.8892 −2.47936
\(439\) 24.8183 1.18451 0.592256 0.805750i \(-0.298237\pi\)
0.592256 + 0.805750i \(0.298237\pi\)
\(440\) 5.68186 0.270872
\(441\) −40.1742 −1.91306
\(442\) 1.10773 0.0526893
\(443\) −28.6854 −1.36289 −0.681443 0.731871i \(-0.738647\pi\)
−0.681443 + 0.731871i \(0.738647\pi\)
\(444\) −64.3822 −3.05544
\(445\) 6.85878 0.325138
\(446\) −24.5867 −1.16421
\(447\) −68.5807 −3.24376
\(448\) −14.3536 −0.678145
\(449\) −34.0314 −1.60604 −0.803020 0.595952i \(-0.796775\pi\)
−0.803020 + 0.595952i \(0.796775\pi\)
\(450\) −15.7439 −0.742176
\(451\) −0.971313 −0.0457373
\(452\) −13.3097 −0.626034
\(453\) 9.37659 0.440551
\(454\) 20.6208 0.967781
\(455\) −6.81462 −0.319474
\(456\) 3.80084 0.177990
\(457\) 38.9855 1.82367 0.911833 0.410562i \(-0.134667\pi\)
0.911833 + 0.410562i \(0.134667\pi\)
\(458\) −5.46386 −0.255309
\(459\) −1.37346 −0.0641075
\(460\) 6.46873 0.301606
\(461\) 19.9090 0.927255 0.463627 0.886030i \(-0.346548\pi\)
0.463627 + 0.886030i \(0.346548\pi\)
\(462\) −45.5822 −2.12068
\(463\) 21.0581 0.978651 0.489325 0.872101i \(-0.337243\pi\)
0.489325 + 0.872101i \(0.337243\pi\)
\(464\) 26.4720 1.22893
\(465\) 18.5166 0.858688
\(466\) 26.2578 1.21637
\(467\) −2.19932 −0.101772 −0.0508862 0.998704i \(-0.516205\pi\)
−0.0508862 + 0.998704i \(0.516205\pi\)
\(468\) −100.669 −4.65341
\(469\) −4.35948 −0.201302
\(470\) −23.5803 −1.08768
\(471\) 34.4175 1.58587
\(472\) 0.782665 0.0360251
\(473\) −46.6603 −2.14544
\(474\) 106.827 4.90672
\(475\) 1.09592 0.0502842
\(476\) 0.303842 0.0139266
\(477\) 31.6399 1.44869
\(478\) −48.3349 −2.21079
\(479\) 4.79525 0.219101 0.109550 0.993981i \(-0.465059\pi\)
0.109550 + 0.993981i \(0.465059\pi\)
\(480\) −25.6494 −1.17073
\(481\) −43.1076 −1.96554
\(482\) 4.59853 0.209457
\(483\) −10.4818 −0.476940
\(484\) 42.5005 1.93184
\(485\) 2.35225 0.106810
\(486\) 71.9843 3.26527
\(487\) −31.9873 −1.44948 −0.724741 0.689021i \(-0.758041\pi\)
−0.724741 + 0.689021i \(0.758041\pi\)
\(488\) −0.00993420 −0.000449700 0
\(489\) −39.9451 −1.80638
\(490\) 11.4986 0.519455
\(491\) 14.1151 0.637007 0.318503 0.947922i \(-0.396820\pi\)
0.318503 + 0.947922i \(0.396820\pi\)
\(492\) −1.48589 −0.0669892
\(493\) −0.933837 −0.0420579
\(494\) 12.5995 0.566878
\(495\) −39.2158 −1.76262
\(496\) 15.6701 0.703608
\(497\) −8.96518 −0.402143
\(498\) 69.2143 3.10157
\(499\) −33.9271 −1.51878 −0.759392 0.650633i \(-0.774504\pi\)
−0.759392 + 0.650633i \(0.774504\pi\)
\(500\) 2.50621 0.112081
\(501\) 50.4673 2.25471
\(502\) 26.4365 1.17992
\(503\) −13.9526 −0.622118 −0.311059 0.950391i \(-0.600684\pi\)
−0.311059 + 0.950391i \(0.600684\pi\)
\(504\) −10.0281 −0.446685
\(505\) −2.37026 −0.105475
\(506\) 28.9708 1.28791
\(507\) −52.7107 −2.34096
\(508\) −4.68478 −0.207853
\(509\) 12.7429 0.564819 0.282410 0.959294i \(-0.408866\pi\)
0.282410 + 0.959294i \(0.408866\pi\)
\(510\) 0.660128 0.0292310
\(511\) −9.52970 −0.421569
\(512\) −27.5764 −1.21872
\(513\) −15.6219 −0.689725
\(514\) −60.4548 −2.66655
\(515\) 16.8025 0.740406
\(516\) −71.3799 −3.14232
\(517\) −58.7351 −2.58317
\(518\) −21.2599 −0.934108
\(519\) 35.7516 1.56932
\(520\) 5.81978 0.255214
\(521\) −32.4044 −1.41966 −0.709831 0.704372i \(-0.751229\pi\)
−0.709831 + 0.704372i \(0.751229\pi\)
\(522\) 152.590 6.67867
\(523\) −4.56133 −0.199453 −0.0997265 0.995015i \(-0.531797\pi\)
−0.0997265 + 0.995015i \(0.531797\pi\)
\(524\) −28.8659 −1.26101
\(525\) −4.06103 −0.177238
\(526\) 38.8060 1.69202
\(527\) −0.552785 −0.0240797
\(528\) −46.6113 −2.02850
\(529\) −16.3380 −0.710349
\(530\) −9.05593 −0.393364
\(531\) −5.40189 −0.234422
\(532\) 3.45595 0.149835
\(533\) −0.994890 −0.0430935
\(534\) 46.9912 2.03351
\(535\) −16.2024 −0.700491
\(536\) 3.72305 0.160811
\(537\) −36.7836 −1.58733
\(538\) −15.4905 −0.667843
\(539\) 28.6414 1.23367
\(540\) −35.7251 −1.53736
\(541\) 1.74553 0.0750464 0.0375232 0.999296i \(-0.488053\pi\)
0.0375232 + 0.999296i \(0.488053\pi\)
\(542\) −27.8793 −1.19752
\(543\) −22.4461 −0.963255
\(544\) 0.765722 0.0328301
\(545\) −14.4627 −0.619514
\(546\) −46.6887 −1.99809
\(547\) 20.7430 0.886908 0.443454 0.896297i \(-0.353753\pi\)
0.443454 + 0.896297i \(0.353753\pi\)
\(548\) −1.67300 −0.0714671
\(549\) 0.0685651 0.00292629
\(550\) 11.2243 0.478606
\(551\) −10.6216 −0.452496
\(552\) 8.95164 0.381007
\(553\) 19.6193 0.834296
\(554\) −26.8342 −1.14008
\(555\) −25.6890 −1.09044
\(556\) 22.5158 0.954881
\(557\) −30.0010 −1.27118 −0.635591 0.772026i \(-0.719244\pi\)
−0.635591 + 0.772026i \(0.719244\pi\)
\(558\) 90.3256 3.82379
\(559\) −47.7929 −2.02143
\(560\) −3.43674 −0.145229
\(561\) 1.64428 0.0694216
\(562\) 15.2002 0.641183
\(563\) −38.1608 −1.60829 −0.804144 0.594435i \(-0.797376\pi\)
−0.804144 + 0.594435i \(0.797376\pi\)
\(564\) −89.8516 −3.78343
\(565\) −5.31068 −0.223422
\(566\) −6.85025 −0.287938
\(567\) 29.8922 1.25535
\(568\) 7.65639 0.321255
\(569\) −32.9653 −1.38198 −0.690988 0.722866i \(-0.742824\pi\)
−0.690988 + 0.722866i \(0.742824\pi\)
\(570\) 7.50841 0.314493
\(571\) 1.51322 0.0633264 0.0316632 0.999499i \(-0.489920\pi\)
0.0316632 + 0.999499i \(0.489920\pi\)
\(572\) 71.7696 3.00084
\(573\) −15.8298 −0.661298
\(574\) −0.490663 −0.0204799
\(575\) 2.58108 0.107638
\(576\) −84.6052 −3.52521
\(577\) 1.75534 0.0730758 0.0365379 0.999332i \(-0.488367\pi\)
0.0365379 + 0.999332i \(0.488367\pi\)
\(578\) 36.0676 1.50022
\(579\) −10.0940 −0.419493
\(580\) −24.2901 −1.00859
\(581\) 12.7116 0.527364
\(582\) 16.1159 0.668024
\(583\) −22.5570 −0.934214
\(584\) 8.13850 0.336773
\(585\) −40.1677 −1.66073
\(586\) −8.99210 −0.371460
\(587\) 19.0952 0.788142 0.394071 0.919080i \(-0.371066\pi\)
0.394071 + 0.919080i \(0.371066\pi\)
\(588\) 43.8149 1.80690
\(589\) −6.28747 −0.259071
\(590\) 1.54612 0.0636529
\(591\) 48.9147 2.01208
\(592\) −21.7399 −0.893506
\(593\) −26.0877 −1.07129 −0.535646 0.844442i \(-0.679932\pi\)
−0.535646 + 0.844442i \(0.679932\pi\)
\(594\) −159.998 −6.56481
\(595\) 0.121236 0.00497018
\(596\) 53.2544 2.18139
\(597\) −74.0657 −3.03131
\(598\) 29.6740 1.21346
\(599\) 13.2440 0.541133 0.270567 0.962701i \(-0.412789\pi\)
0.270567 + 0.962701i \(0.412789\pi\)
\(600\) 3.46818 0.141588
\(601\) 19.8113 0.808120 0.404060 0.914733i \(-0.367599\pi\)
0.404060 + 0.914733i \(0.367599\pi\)
\(602\) −23.5707 −0.960669
\(603\) −25.6962 −1.04643
\(604\) −7.28113 −0.296265
\(605\) 16.9581 0.689443
\(606\) −16.2393 −0.659675
\(607\) 31.2565 1.26866 0.634331 0.773061i \(-0.281275\pi\)
0.634331 + 0.773061i \(0.281275\pi\)
\(608\) 8.70945 0.353215
\(609\) 39.3594 1.59492
\(610\) −0.0196246 −0.000794578 0
\(611\) −60.1608 −2.43385
\(612\) 1.79095 0.0723949
\(613\) 45.3983 1.83362 0.916810 0.399323i \(-0.130755\pi\)
0.916810 + 0.399323i \(0.130755\pi\)
\(614\) −5.31147 −0.214354
\(615\) −0.592884 −0.0239074
\(616\) 7.14929 0.288053
\(617\) −34.2262 −1.37789 −0.688947 0.724812i \(-0.741927\pi\)
−0.688947 + 0.724812i \(0.741927\pi\)
\(618\) 115.118 4.63073
\(619\) −11.4086 −0.458549 −0.229274 0.973362i \(-0.573635\pi\)
−0.229274 + 0.973362i \(0.573635\pi\)
\(620\) −14.3786 −0.577457
\(621\) −36.7924 −1.47643
\(622\) −15.1513 −0.607513
\(623\) 8.63017 0.345760
\(624\) −47.7428 −1.91124
\(625\) 1.00000 0.0400000
\(626\) −34.1522 −1.36500
\(627\) 18.7023 0.746899
\(628\) −26.7259 −1.06648
\(629\) 0.766907 0.0305786
\(630\) −19.8100 −0.789251
\(631\) 41.9627 1.67051 0.835254 0.549864i \(-0.185320\pi\)
0.835254 + 0.549864i \(0.185320\pi\)
\(632\) −16.7551 −0.666483
\(633\) −7.59911 −0.302038
\(634\) −45.8433 −1.82067
\(635\) −1.86927 −0.0741796
\(636\) −34.5071 −1.36830
\(637\) 29.3366 1.16236
\(638\) −108.786 −4.30686
\(639\) −52.8438 −2.09047
\(640\) 8.32125 0.328926
\(641\) 37.2796 1.47246 0.736228 0.676734i \(-0.236605\pi\)
0.736228 + 0.676734i \(0.236605\pi\)
\(642\) −111.007 −4.38108
\(643\) 44.6128 1.75936 0.879679 0.475567i \(-0.157757\pi\)
0.879679 + 0.475567i \(0.157757\pi\)
\(644\) 8.13938 0.320736
\(645\) −28.4812 −1.12145
\(646\) −0.224152 −0.00881914
\(647\) 37.2753 1.46544 0.732721 0.680529i \(-0.238250\pi\)
0.732721 + 0.680529i \(0.238250\pi\)
\(648\) −25.5284 −1.00285
\(649\) 3.85117 0.151171
\(650\) 11.4968 0.450940
\(651\) 23.2988 0.913153
\(652\) 31.0183 1.21477
\(653\) −16.1199 −0.630819 −0.315409 0.948956i \(-0.602142\pi\)
−0.315409 + 0.948956i \(0.602142\pi\)
\(654\) −99.0875 −3.87463
\(655\) −11.5178 −0.450036
\(656\) −0.501741 −0.0195897
\(657\) −56.1713 −2.19145
\(658\) −29.6703 −1.15667
\(659\) 10.0809 0.392696 0.196348 0.980534i \(-0.437092\pi\)
0.196348 + 0.980534i \(0.437092\pi\)
\(660\) 42.7696 1.66480
\(661\) 5.28707 0.205643 0.102822 0.994700i \(-0.467213\pi\)
0.102822 + 0.994700i \(0.467213\pi\)
\(662\) −33.0352 −1.28395
\(663\) 1.68419 0.0654087
\(664\) −10.8558 −0.421288
\(665\) 1.37896 0.0534736
\(666\) −125.313 −4.85579
\(667\) −25.0158 −0.968614
\(668\) −39.1890 −1.51627
\(669\) −37.3816 −1.44526
\(670\) 7.35475 0.284139
\(671\) −0.0488820 −0.00188707
\(672\) −32.2737 −1.24499
\(673\) 30.5104 1.17609 0.588045 0.808828i \(-0.299898\pi\)
0.588045 + 0.808828i \(0.299898\pi\)
\(674\) 52.2971 2.01441
\(675\) −14.2546 −0.548661
\(676\) 40.9310 1.57427
\(677\) −35.3014 −1.35674 −0.678372 0.734719i \(-0.737314\pi\)
−0.678372 + 0.734719i \(0.737314\pi\)
\(678\) −36.3847 −1.39735
\(679\) 2.95976 0.113585
\(680\) −0.103537 −0.00397046
\(681\) 31.3518 1.20141
\(682\) −64.3957 −2.46584
\(683\) 10.7946 0.413044 0.206522 0.978442i \(-0.433785\pi\)
0.206522 + 0.978442i \(0.433785\pi\)
\(684\) 20.3706 0.778888
\(685\) −0.667543 −0.0255055
\(686\) 33.1655 1.26626
\(687\) −8.30726 −0.316942
\(688\) −24.1028 −0.918912
\(689\) −23.1045 −0.880212
\(690\) 17.6836 0.673204
\(691\) −16.3414 −0.621655 −0.310827 0.950466i \(-0.600606\pi\)
−0.310827 + 0.950466i \(0.600606\pi\)
\(692\) −27.7619 −1.05535
\(693\) −49.3439 −1.87442
\(694\) −13.4274 −0.509697
\(695\) 8.98399 0.340782
\(696\) −33.6135 −1.27412
\(697\) 0.0176996 0.000670422 0
\(698\) 27.2673 1.03208
\(699\) 39.9224 1.51000
\(700\) 3.15348 0.119190
\(701\) 8.14575 0.307661 0.153830 0.988097i \(-0.450839\pi\)
0.153830 + 0.988097i \(0.450839\pi\)
\(702\) −163.882 −6.18533
\(703\) 8.72293 0.328991
\(704\) 60.3174 2.27330
\(705\) −35.8516 −1.35025
\(706\) −8.99329 −0.338467
\(707\) −2.98242 −0.112165
\(708\) 5.89142 0.221413
\(709\) −41.0461 −1.54152 −0.770759 0.637126i \(-0.780123\pi\)
−0.770759 + 0.637126i \(0.780123\pi\)
\(710\) 15.1249 0.567627
\(711\) 115.643 4.33694
\(712\) −7.37028 −0.276213
\(713\) −14.8081 −0.554568
\(714\) 0.830616 0.0310850
\(715\) 28.6367 1.07095
\(716\) 28.5632 1.06746
\(717\) −73.4884 −2.74447
\(718\) −52.9264 −1.97520
\(719\) −8.18794 −0.305359 −0.152679 0.988276i \(-0.548790\pi\)
−0.152679 + 0.988276i \(0.548790\pi\)
\(720\) −20.2573 −0.754945
\(721\) 21.1420 0.787369
\(722\) 37.7834 1.40615
\(723\) 6.99161 0.260021
\(724\) 17.4299 0.647777
\(725\) −9.69197 −0.359951
\(726\) 116.184 4.31199
\(727\) 8.45191 0.313464 0.156732 0.987641i \(-0.449904\pi\)
0.156732 + 0.987641i \(0.449904\pi\)
\(728\) 7.32283 0.271402
\(729\) 38.1750 1.41389
\(730\) 16.0773 0.595047
\(731\) 0.850262 0.0314481
\(732\) −0.0747786 −0.00276390
\(733\) −32.6343 −1.20538 −0.602688 0.797977i \(-0.705904\pi\)
−0.602688 + 0.797977i \(0.705904\pi\)
\(734\) −10.7725 −0.397620
\(735\) 17.4825 0.644853
\(736\) 20.5123 0.756093
\(737\) 18.3196 0.674811
\(738\) −2.89214 −0.106461
\(739\) −38.9034 −1.43108 −0.715542 0.698570i \(-0.753820\pi\)
−0.715542 + 0.698570i \(0.753820\pi\)
\(740\) 19.9481 0.733307
\(741\) 19.1563 0.703724
\(742\) −11.3948 −0.418315
\(743\) −35.0291 −1.28509 −0.642547 0.766246i \(-0.722122\pi\)
−0.642547 + 0.766246i \(0.722122\pi\)
\(744\) −19.8975 −0.729478
\(745\) 21.2490 0.778502
\(746\) −25.7615 −0.943196
\(747\) 74.9262 2.74141
\(748\) −1.27682 −0.0466852
\(749\) −20.3869 −0.744922
\(750\) 6.85125 0.250172
\(751\) 24.1673 0.881876 0.440938 0.897537i \(-0.354646\pi\)
0.440938 + 0.897537i \(0.354646\pi\)
\(752\) −30.3402 −1.10639
\(753\) 40.1940 1.46475
\(754\) −111.426 −4.05790
\(755\) −2.90523 −0.105732
\(756\) −44.9517 −1.63488
\(757\) −13.5261 −0.491614 −0.245807 0.969319i \(-0.579053\pi\)
−0.245807 + 0.969319i \(0.579053\pi\)
\(758\) 70.4717 2.55965
\(759\) 44.0473 1.59881
\(760\) −1.17765 −0.0427178
\(761\) −14.6317 −0.530398 −0.265199 0.964194i \(-0.585438\pi\)
−0.265199 + 0.964194i \(0.585438\pi\)
\(762\) −12.8068 −0.463942
\(763\) −18.1979 −0.658809
\(764\) 12.2922 0.444715
\(765\) 0.714605 0.0258366
\(766\) −28.7664 −1.03937
\(767\) 3.94465 0.142433
\(768\) −16.6239 −0.599863
\(769\) −24.4642 −0.882202 −0.441101 0.897457i \(-0.645412\pi\)
−0.441101 + 0.897457i \(0.645412\pi\)
\(770\) 14.1231 0.508963
\(771\) −91.9155 −3.31025
\(772\) 7.83822 0.282104
\(773\) 7.20675 0.259209 0.129604 0.991566i \(-0.458629\pi\)
0.129604 + 0.991566i \(0.458629\pi\)
\(774\) −138.934 −4.99387
\(775\) −5.73717 −0.206085
\(776\) −2.52767 −0.0907382
\(777\) −32.3236 −1.15960
\(778\) 61.9796 2.22208
\(779\) 0.201319 0.00721299
\(780\) 43.8078 1.56857
\(781\) 37.6739 1.34808
\(782\) −0.527917 −0.0188783
\(783\) 138.156 4.93728
\(784\) 14.7950 0.528392
\(785\) −10.6639 −0.380610
\(786\) −78.9110 −2.81466
\(787\) 11.0720 0.394675 0.197337 0.980336i \(-0.436771\pi\)
0.197337 + 0.980336i \(0.436771\pi\)
\(788\) −37.9833 −1.35310
\(789\) 59.0006 2.10048
\(790\) −33.0991 −1.17761
\(791\) −6.68224 −0.237593
\(792\) 42.1403 1.49739
\(793\) −0.0500686 −0.00177799
\(794\) −6.93938 −0.246269
\(795\) −13.7686 −0.488323
\(796\) 57.5136 2.03852
\(797\) 23.6826 0.838882 0.419441 0.907782i \(-0.362226\pi\)
0.419441 + 0.907782i \(0.362226\pi\)
\(798\) 9.44757 0.334440
\(799\) 1.07029 0.0378643
\(800\) 7.94717 0.280975
\(801\) 50.8692 1.79737
\(802\) 57.0092 2.01306
\(803\) 40.0461 1.41320
\(804\) 28.0249 0.988361
\(805\) 3.24768 0.114466
\(806\) −65.9589 −2.32330
\(807\) −23.5518 −0.829062
\(808\) 2.54703 0.0896042
\(809\) −5.48103 −0.192703 −0.0963513 0.995347i \(-0.530717\pi\)
−0.0963513 + 0.995347i \(0.530717\pi\)
\(810\) −50.4303 −1.77194
\(811\) −4.58657 −0.161056 −0.0805281 0.996752i \(-0.525661\pi\)
−0.0805281 + 0.996752i \(0.525661\pi\)
\(812\) −30.5634 −1.07257
\(813\) −42.3877 −1.48660
\(814\) 89.3395 3.13135
\(815\) 12.3766 0.433532
\(816\) 0.849369 0.0297339
\(817\) 9.67102 0.338346
\(818\) 75.8766 2.65296
\(819\) −50.5416 −1.76607
\(820\) 0.460387 0.0160774
\(821\) −9.89963 −0.345499 −0.172750 0.984966i \(-0.555265\pi\)
−0.172750 + 0.984966i \(0.555265\pi\)
\(822\) −4.57350 −0.159519
\(823\) −13.3376 −0.464919 −0.232459 0.972606i \(-0.574677\pi\)
−0.232459 + 0.972606i \(0.574677\pi\)
\(824\) −18.0556 −0.628995
\(825\) 17.0654 0.594142
\(826\) 1.94543 0.0676903
\(827\) −2.71638 −0.0944576 −0.0472288 0.998884i \(-0.515039\pi\)
−0.0472288 + 0.998884i \(0.515039\pi\)
\(828\) 47.9763 1.66729
\(829\) 22.0724 0.766607 0.383303 0.923623i \(-0.374786\pi\)
0.383303 + 0.923623i \(0.374786\pi\)
\(830\) −21.4453 −0.744377
\(831\) −40.7987 −1.41529
\(832\) 61.7816 2.14189
\(833\) −0.521914 −0.0180832
\(834\) 61.5515 2.13136
\(835\) −15.6367 −0.541132
\(836\) −14.5228 −0.502280
\(837\) 81.7813 2.82678
\(838\) 27.4823 0.949359
\(839\) −51.7389 −1.78623 −0.893113 0.449832i \(-0.851484\pi\)
−0.893113 + 0.449832i \(0.851484\pi\)
\(840\) 4.36388 0.150568
\(841\) 64.9344 2.23912
\(842\) −49.8943 −1.71947
\(843\) 23.1105 0.795966
\(844\) 5.90088 0.203117
\(845\) 16.3318 0.561832
\(846\) −174.887 −6.01274
\(847\) 21.3377 0.733173
\(848\) −11.6520 −0.400132
\(849\) −10.4151 −0.357446
\(850\) −0.204533 −0.00701544
\(851\) 20.5440 0.704240
\(852\) 57.6326 1.97446
\(853\) 21.9675 0.752154 0.376077 0.926588i \(-0.377273\pi\)
0.376077 + 0.926588i \(0.377273\pi\)
\(854\) −0.0246930 −0.000844977 0
\(855\) 8.12803 0.277973
\(856\) 17.4107 0.595086
\(857\) 36.4401 1.24477 0.622386 0.782711i \(-0.286164\pi\)
0.622386 + 0.782711i \(0.286164\pi\)
\(858\) 196.197 6.69806
\(859\) 36.3576 1.24050 0.620252 0.784402i \(-0.287030\pi\)
0.620252 + 0.784402i \(0.287030\pi\)
\(860\) 22.1163 0.754158
\(861\) −0.746005 −0.0254238
\(862\) 7.57174 0.257895
\(863\) 8.07008 0.274709 0.137354 0.990522i \(-0.456140\pi\)
0.137354 + 0.990522i \(0.456140\pi\)
\(864\) −113.284 −3.85400
\(865\) −11.0772 −0.376637
\(866\) 7.64792 0.259887
\(867\) 54.8372 1.86237
\(868\) −18.0920 −0.614084
\(869\) −82.4450 −2.79675
\(870\) −66.4021 −2.25124
\(871\) 18.7643 0.635803
\(872\) 15.5413 0.526294
\(873\) 17.4458 0.590452
\(874\) −6.00462 −0.203109
\(875\) 1.25827 0.0425371
\(876\) 61.2616 2.06984
\(877\) 49.0605 1.65666 0.828328 0.560243i \(-0.189292\pi\)
0.828328 + 0.560243i \(0.189292\pi\)
\(878\) −52.6839 −1.77799
\(879\) −13.6716 −0.461132
\(880\) 14.4420 0.486840
\(881\) 28.2067 0.950306 0.475153 0.879903i \(-0.342393\pi\)
0.475153 + 0.879903i \(0.342393\pi\)
\(882\) 85.2812 2.87157
\(883\) −11.9826 −0.403248 −0.201624 0.979463i \(-0.564622\pi\)
−0.201624 + 0.979463i \(0.564622\pi\)
\(884\) −1.30781 −0.0439865
\(885\) 2.35073 0.0790189
\(886\) 60.8930 2.04574
\(887\) −0.691065 −0.0232037 −0.0116018 0.999933i \(-0.503693\pi\)
−0.0116018 + 0.999933i \(0.503693\pi\)
\(888\) 27.6048 0.926358
\(889\) −2.35203 −0.0788847
\(890\) −14.5597 −0.488043
\(891\) −125.614 −4.20824
\(892\) 29.0276 0.971917
\(893\) 12.1737 0.407377
\(894\) 145.582 4.86899
\(895\) 11.3970 0.380959
\(896\) 10.4703 0.349789
\(897\) 45.1164 1.50639
\(898\) 72.2412 2.41072
\(899\) 55.6045 1.85451
\(900\) 18.5877 0.619589
\(901\) 0.411042 0.0136938
\(902\) 2.06189 0.0686533
\(903\) −35.8369 −1.19258
\(904\) 5.70672 0.189803
\(905\) 6.95468 0.231181
\(906\) −19.9045 −0.661282
\(907\) −14.7332 −0.489209 −0.244604 0.969623i \(-0.578658\pi\)
−0.244604 + 0.969623i \(0.578658\pi\)
\(908\) −24.3454 −0.807930
\(909\) −17.5794 −0.583072
\(910\) 14.4660 0.479542
\(911\) 2.58914 0.0857819 0.0428909 0.999080i \(-0.486343\pi\)
0.0428909 + 0.999080i \(0.486343\pi\)
\(912\) 9.66087 0.319903
\(913\) −53.4171 −1.76785
\(914\) −82.7578 −2.73739
\(915\) −0.0298373 −0.000986391 0
\(916\) 6.45077 0.213139
\(917\) −14.4924 −0.478581
\(918\) 2.91555 0.0962275
\(919\) −11.2402 −0.370781 −0.185390 0.982665i \(-0.559355\pi\)
−0.185390 + 0.982665i \(0.559355\pi\)
\(920\) −2.77357 −0.0914418
\(921\) −8.07557 −0.266099
\(922\) −42.2625 −1.39184
\(923\) 38.5884 1.27015
\(924\) 53.8155 1.77040
\(925\) 7.95947 0.261706
\(926\) −44.7017 −1.46899
\(927\) 124.618 4.09300
\(928\) −77.0238 −2.52843
\(929\) 41.9325 1.37576 0.687881 0.725823i \(-0.258541\pi\)
0.687881 + 0.725823i \(0.258541\pi\)
\(930\) −39.3068 −1.28892
\(931\) −5.93633 −0.194556
\(932\) −31.0006 −1.01546
\(933\) −23.0361 −0.754169
\(934\) 4.66868 0.152764
\(935\) −0.509462 −0.0166612
\(936\) 43.1632 1.41083
\(937\) 22.5067 0.735261 0.367630 0.929972i \(-0.380169\pi\)
0.367630 + 0.929972i \(0.380169\pi\)
\(938\) 9.25423 0.302161
\(939\) −51.9250 −1.69451
\(940\) 27.8395 0.908025
\(941\) −45.7175 −1.49035 −0.745173 0.666871i \(-0.767633\pi\)
−0.745173 + 0.666871i \(0.767633\pi\)
\(942\) −73.0609 −2.38045
\(943\) 0.474141 0.0154401
\(944\) 1.98936 0.0647480
\(945\) −17.9361 −0.583462
\(946\) 99.0498 3.22039
\(947\) 36.7431 1.19399 0.596995 0.802245i \(-0.296361\pi\)
0.596995 + 0.802245i \(0.296361\pi\)
\(948\) −126.122 −4.09627
\(949\) 41.0182 1.33151
\(950\) −2.32640 −0.0754783
\(951\) −69.7002 −2.26018
\(952\) −0.130277 −0.00422230
\(953\) 46.8178 1.51658 0.758288 0.651919i \(-0.226036\pi\)
0.758288 + 0.651919i \(0.226036\pi\)
\(954\) −67.1646 −2.17453
\(955\) 4.90468 0.158712
\(956\) 57.0653 1.84562
\(957\) −165.398 −5.34655
\(958\) −10.1793 −0.328878
\(959\) −0.839946 −0.0271233
\(960\) 36.8174 1.18828
\(961\) 1.91514 0.0617786
\(962\) 91.5081 2.95034
\(963\) −120.167 −3.87234
\(964\) −5.42914 −0.174861
\(965\) 3.12752 0.100678
\(966\) 22.2507 0.715904
\(967\) 14.3053 0.460026 0.230013 0.973188i \(-0.426123\pi\)
0.230013 + 0.973188i \(0.426123\pi\)
\(968\) −18.2227 −0.585701
\(969\) −0.340801 −0.0109481
\(970\) −4.99332 −0.160326
\(971\) −14.8605 −0.476896 −0.238448 0.971155i \(-0.576639\pi\)
−0.238448 + 0.971155i \(0.576639\pi\)
\(972\) −84.9864 −2.72594
\(973\) 11.3042 0.362397
\(974\) 67.9021 2.17572
\(975\) 17.4797 0.559798
\(976\) −0.0252505 −0.000808249 0
\(977\) −10.7287 −0.343241 −0.171621 0.985163i \(-0.554900\pi\)
−0.171621 + 0.985163i \(0.554900\pi\)
\(978\) 84.7948 2.71144
\(979\) −36.2661 −1.15907
\(980\) −13.5756 −0.433655
\(981\) −107.265 −3.42470
\(982\) −29.9633 −0.956169
\(983\) −48.6123 −1.55049 −0.775245 0.631660i \(-0.782374\pi\)
−0.775245 + 0.631660i \(0.782374\pi\)
\(984\) 0.637099 0.0203100
\(985\) −15.1557 −0.482900
\(986\) 1.98233 0.0631303
\(987\) −45.1108 −1.43589
\(988\) −14.8753 −0.473246
\(989\) 22.7770 0.724265
\(990\) 83.2466 2.64575
\(991\) −3.88438 −0.123392 −0.0616958 0.998095i \(-0.519651\pi\)
−0.0616958 + 0.998095i \(0.519651\pi\)
\(992\) −45.5943 −1.44762
\(993\) −50.2268 −1.59390
\(994\) 19.0311 0.603631
\(995\) 22.9484 0.727514
\(996\) −81.7162 −2.58928
\(997\) −36.4306 −1.15377 −0.576885 0.816825i \(-0.695732\pi\)
−0.576885 + 0.816825i \(0.695732\pi\)
\(998\) 72.0198 2.27975
\(999\) −113.459 −3.58970
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8035.2.a.b.1.19 114
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8035.2.a.b.1.19 114 1.1 even 1 trivial